Wednesday, September 30, 2009

Jonathan Dowling from Louisiana State University gave a presentation about the use of entangled photons for high precision interferometry [1] showing that they can lead to much better measurements than it is possible with classical light. These entangled photon states are of the formSome problems remain such as the difficulty to produce NOON states with high power, but they are very promising anyway.

So far they devised how to make ingenious conditional measurements in order to generate NOON states.

Another important topic was the emulation of non-linear effects by conditional measurements within linear optics [2].

Saturday, September 26, 2009

Humans have 23 chromosomes while all the other hominids have 24 chromosomes. The question is, how can this be possible if we are suppose to have a common ancestor. Now we know that human chromosome 2 is the result of the fusion of two chromosomes found in our relative hominids.YouTube:Chromosome 2

Friday, September 25, 2009

Kurt Jacobs gave a presentation about Quantum Feedback Control. He showed how to introduce the action of weak continuous measurements into a master equation that. This equation resembles the Lindblad equation with an extra stochastic term, where the feedback can be introduced in the Hamiltonian. One application was to create a cat state of a harmonic oscillator.

For low dimensions it was shown that the adiabatic quantum computer is polynomial, for a certain problem with exponential complexity in a classical computer. Peter Young, who gave a presentation at Princeton yesterday, is using Quantum Montecarlo Simuations, as used in statistical mechanics for the partition function, in order to engage this problem for higher dimensions where direct simulations are not feasible.The Complexity Of The Quantum Adiabatic Algorithm

I want to write equations in my blog, so I found mimetex, but I could not run it from the cgi Princeton server. I do not know why. I may need to set up complicated permissions or there is a compatibility issue between mimetex and the cgi server.

Here I am testing the cgi provided by mimetex

It works, but I can only use it as a test.

Another method, less elegant though, is using MathTran, which I used to make the following equation

My presentation is going to be about my package developed for performing Magnus expansions. This expansion can be used to find approximate solutions for systems of linear equations and linear operators in general

This method is based in the measurement of the Bures distance between a given state and the closest separable state, which allows one to calculate the generalized Schmidt state. The entanglement can be measured from the coefficients of this Schmidt state.

This paper shows how the Bures measure can be expressed as the product of the measure of even euclidean balls. This means that we now have a simple and easy formula for sampling. The ultimate application will be in Bayesian quantum estimation.

The technology of transmission of information between multiple antennas began to develop 10 years ago. The purpose is to increase the fidelity and transmission rate between multiple sources and multiple receptors.

The particular technology that I am interested mostly is in the Unitary Space-Time Codes (UST). In this technology, the information is encoded in blocks spanning space and time. In the simplest case, we could think of N antennas with a sequence of N pulses, so that the information block can be represented as an NxN complex matrix. It is mathematically convenient to use unitary matrices, so the name UST is justified in this case.

Inside the UST field I am paying attention to the Cayley encoding [1,2,3] because it seems to be elegant, simple and easy to understand.